10
29
(K10a
53
)
A knot diagram
1
Linearized knot diagam
8 1 6 9 10 3 2 7 5 4
Solving Sequence
6,10
5 9 4 1 3 7 2 8
c
5
c
9
c
4
c
10
c
3
c
6
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
31
+ u
30
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 31 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hu
31
+ u
30
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
−u
2
a
9
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
7
=
u
8
− 3u
6
+ u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
2
=
−u
16
+ 7u
14
− 19u
12
+ 24u
10
− 13u
8
+ 2u
6
− 2u
4
+ 2u
2
+ 1
u
18
− 8u
16
+ 25u
14
− 36u
12
+ 19u
10
+ 4u
8
− 2u
6
− 2u
4
− 3u
2
a
8
=
−u
19
+ 8u
17
− 24u
15
+ 30u
13
− 7u
11
− 10u
9
− 4u
7
+ 6u
5
+ 3u
3
+ 2u
u
19
− 9u
17
+ 32u
15
− 55u
13
+ 43u
11
− 9u
9
− 4u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
28
− 52u
26
+ 4u
25
+ 292u
24
− 48u
23
− 916u
22
+ 244u
21
+
1732u
20
− 672u
19
− 1988u
18
+ 1056u
17
+ 1360u
16
− 896u
15
− 644u
14
+ 332u
13
+
420u
12
− 60u
11
− 288u
10
+ 84u
9
+ 88u
8
− 16u
6
− 44u
5
+ 4u
2
− 16u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
31
− u
30
+ ··· + 2u
2
+ 1
c
2
, c
8
u
31
+ 11u
30
+ ··· − 4u − 1
c
3
, c
6
u
31
+ 5u
30
+ ··· + 40u + 7
c
4
, c
5
, c
9
u
31
+ u
30
+ ··· + 2u + 1
c
10
u
31
− 3u
30
+ ··· − 13u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
31
+ 11y
30
+ ··· − 4y −1
c
2
, c
8
y
31
+ 19y
30
+ ··· − 8y −1
c
3
, c
6
y
31
+ 23y
30
+ ··· − 640y −49
c
4
, c
5
, c
9
y
31
− 29y
30
+ ··· − 4y −1
c
10
y
31
− 9y
30
+ ··· + 1481y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.196790 + 0.189244I
0.502956 + 0.402984I −0.929300 − 0.528315I
u = −1.196790 − 0.189244I
0.502956 − 0.402984I −0.929300 + 0.528315I
u = 0.371332 + 0.681959I
−0.47562 − 8.17190I −2.44268 + 8.00325I
u = 0.371332 − 0.681959I
−0.47562 + 8.17190I −2.44268 − 8.00325I
u = 0.434998 + 0.611250I
−4.89690 − 1.99617I −7.89924 + 3.62729I
u = 0.434998 − 0.611250I
−4.89690 + 1.99617I −7.89924 − 3.62729I
u = 1.239060 + 0.217665I
0.12823 − 5.89464I −1.94513 + 6.44091I
u = 1.239060 − 0.217665I
0.12823 + 5.89464I −1.94513 − 6.44091I
u = 0.529247 + 0.517876I
−1.14145 + 4.14236I −4.20039 − 2.04013I
u = 0.529247 − 0.517876I
−1.14145 − 4.14236I −4.20039 + 2.04013I
u = −0.343506 + 0.654959I
0.72976 + 2.73446I −0.23310 − 3.38925I
u = −0.343506 − 0.654959I
0.72976 − 2.73446I −0.23310 + 3.38925I
u = −1.26234
−2.75281 −1.58210
u = −0.028009 + 0.652167I
3.99591 + 2.71284I 3.89942 − 3.44665I
u = −0.028009 − 0.652167I
3.99591 − 2.71284I 3.89942 + 3.44665I
u = 1.358560 + 0.080822I
−5.22411 − 2.56488I −9.16453 + 4.43258I
u = 1.358560 − 0.080822I
−5.22411 + 2.56488I −9.16453 − 4.43258I
u = −0.464772 + 0.428483I
0.007927 + 0.929922I −2.40372 − 3.68841I
u = −0.464772 − 0.428483I
0.007927 − 0.929922I −2.40372 + 3.68841I
u = 1.43568 + 0.18978I
−5.89237 − 3.33239I −5.23670 + 3.21859I
u = 1.43568 − 0.18978I
−5.89237 + 3.33239I −5.23670 − 3.21859I
u = 1.43808 + 0.24908I
−4.99237 − 6.04082I −4.35365 + 3.16093I
u = 1.43808 − 0.24908I
−4.99237 + 6.04082I −4.35365 − 3.16093I
u = −1.45066 + 0.25754I
−6.33335 + 11.60290I −6.34947 − 7.70694I
u = −1.45066 − 0.25754I
−6.33335 − 11.60290I −6.34947 + 7.70694I
u = −1.46473 + 0.17711I
−7.51197 − 1.64856I −8.01509 + 2.12263I
u = −1.46473 − 0.17711I
−7.51197 + 1.64856I −8.01509 − 2.12263I
u = −1.46230 + 0.22292I
−11.00390 + 5.04935I −11.12529 − 3.42516I
u = −1.46230 − 0.22292I
−11.00390 − 5.04935I −11.12529 + 3.42516I
u = −0.265022 + 0.399657I
−0.107136 + 1.026300I −1.81008 − 6.41690I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.265022 − 0.399657I
−0.107136 − 1.026300I −1.81008 + 6.41690I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
31
− u
30
+ ··· + 2u
2
+ 1
c
2
, c
8
u
31
+ 11u
30
+ ··· − 4u − 1
c
3
, c
6
u
31
+ 5u
30
+ ··· + 40u + 7
c
4
, c
5
, c
9
u
31
+ u
30
+ ··· + 2u + 1
c
10
u
31
− 3u
30
+ ··· − 13u − 16
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
31
+ 11y
30
+ ··· − 4y −1
c
2
, c
8
y
31
+ 19y
30
+ ··· − 8y −1
c
3
, c
6
y
31
+ 23y
30
+ ··· − 640y −49
c
4
, c
5
, c
9
y
31
− 29y
30
+ ··· − 4y −1
c
10
y
31
− 9y
30
+ ··· + 1481y −256
8
